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Page 186
... space ( S , Σ , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn , Zn , Mn ) . We write ท Σ = Σ Χ ... ΧΣ μ = μ.Χ ... Χ μην ... measure spaces ( Si , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
... space ( S , Σ , μ ) constructed in Theorem 2 is called the product measure space of the measure spaces ( Sn , Zn , Mn ) . We write ท Σ = Σ Χ ... ΧΣ μ = μ.Χ ... Χ μην ... measure spaces ( Si , 186 III.11.3 III . INTEGRATION AND SET FUNCTIONS.
Page 405
... space s is , of course , the space of all real sequences x [ x ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure Mis countably additive ; the subset l1⁄2 of s is of μ - measure zero ; the ...
... space s is , of course , the space of all real sequences x [ x ] as distinct from l2 , which is the subspace of s determined by the condition < ∞ . The measure Mis countably additive ; the subset l1⁄2 of s is of μ - measure zero ; the ...
Page 725
... space , and let ( S , Z , μ ) be a reg- ular finite measure space . Let o be a mapping of S into itself such that the set { q } of mappings is equicontinuous . Show that p is met- rically transitive if and only if { q'x } is dense in S ...
... space , and let ( S , Z , μ ) be a reg- ular finite measure space . Let o be a mapping of S into itself such that the set { q } of mappings is equicontinuous . Show that p is met- rically transitive if and only if { q'x } is dense in S ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ